For current communication technology, telecommunication or optical fiber communication has been widely used. In the communication method that uses electricity or light, the signal transmission speed is limited below speed of light.
On the other hand, the quantum communication technology or quantum cryptography based on the principle of quantum mechanics is being actively researched.
Moreover, the quantum teleportation, reproducing a quantum state in another system, is also being researched using the entangled state. In the quantum code or the quantum teleportation, the collapse of the wave packet (decoherence) is used. The collapse of the wave packet occurs instantly when measurement is done, and a strong correlation appears in each measurement result of each part in the entangled state.
However, it is said that it is not possible to use the entangled state to send information because an individual measurement result of the entangled state is quite random and we cannot arbitrarily choose the measurement result. Therefore, even in the quantum code or the quantum teleportation, the communication process at the speed below speed of light is needed to actually send information. So the signal transmission speed becomes below speed of light.
U.S. Pat. No. 8,774,641 shows a communication method using the entangled state created from a single-photon state and the cross phase modulation (optical Kerr effect) in the nonlinear optical medium. But it is often the case that a single-photon state is created probably with relatively small probability. So, the sender and the receiver cannot know when the entangled state is created. And it is not easy to keep enough accuracy of communication because a lot of noise can be mixed in the signal.
Related references are as follows:
Quantum States of Light, SpringerBriefs in Mathematical Physics,
DOI 10.1007/978-4-431-55960-3
Prog. Quant. Electr. 1995, Vol. 19, pp.89-130
PRL 93, 250502(2004)
U.S. Pat. No. 8,774,641